Question

Plasmodesmata are cytoplasmic connections across plant cell walls that connect adjacent cell cytoplasms. Some cells have few plasmodesmata connections while others have more; this is due to genetics, age, and location within the plant.

The density of plasmodesmata within the cell membrane ranges from a high of 25 per square micrometer to a low of 0.2 per square micrometer. The average plasmodesmata tube is 40 nm in diameter.

Diagram of plasmodesmata between two plant cells

a. What percentage of the cell membrane surface area is composed of plasmodesmata at the high density? (Assume the area of one end of a plasmodesmal tube is a circle – see image above)    

b. What percentage of the cell membrane surface area is composed of plasmodesmata at the low density?

Answer 1

The density of plasmodesmata within the cell membrane ranges from a high of 25 per square micrometer to a low of 0.2 per square micrometer. The average plasmodesmata tube is 40 nm in diameter.

Approximate diameter of plant cell ranges from 10 to 100 micrometers. For calculation purpose, let’s us assume 50 micrometers to be the diameter of this plant cell. So, radius will be 25 micrometer.

Surface area of plant = 4πr^2

= 4 * 3.14 * 25 * 25 = 7850 micrometer square

Diameter of plasmodesmata tube = 40nm (Radius = 20 * 10^-3micromt.)

25 plasmodesmata are present per square micrometer.

In 7850 square micrometer, number of plasmodesmata present = 7850 * 25 = 196250

Surface area occupied by one plasmodesmata = 4 * 3.14* 20 * 20 * 10^-6 = 0.05 square micrometer.

Surface area occupied by 196250 plasmodesmata = 196250 * 0.05 = 985.96 ~986 square micrometer.

a.

So, at high density, surface area occupied by plasmodesmata = 986 square micrometer.

% occupied by plasmodesmata = (986/7850) * 100 = 12.5%

b.

At low density, number of plasmodesmata = 7850*0.2 = 1570

Surface area occupied by 1570 plasmodesmata = 1570*0.05= 78.5 square micrometer.

% occupied by plasmodesmata at low density = (78.5/7850)*100 = 1%